I generally disagree with just handing over a map, although a crudely-drawn map as @Asher suggested 'from the point of view of a spider' with intentional scaling inaccuracies isn't a bad idea. Better to provide, and constrain, 'what the spider sees' and let the Warlock, and if they choose, the party, do the work to make that meaningful. Instead of letting the 'familiar auto-map' become a de facto disarming of the dungeon and by extension the experience, turn it into another dimension of discovery that enriches the experience.
Along that vein, the situation provides an opportunity to filter anything the imp experiences through the perceptual lens of the imp as well as the familiar relationship - this could serve to ultimately improve the narrative / immersion. Present how a spider would perceive its surroundings rather than how the Warlock would. Maybe it can only see a certain distance and so any room larger than that distance is just a 'large room' of indeterminate size, or impose other creative limitations that restrict its ability to accurately survey the dungeon - if a ceiling is too high, the spider can't see what's on the floor without dropping down, prompting fresh Perception checks if the room is occupied.
Also, leave as many deductions up to the party as possible - obviously you wouldn't say, "Your spider sees a trap in the next room;" if a feature isn't something a spider would naturally notice, decrease the chance that the information is relayed to the warlock - basically NPC the familiar. This gives you complete control over how much is known before the characters enter the dungeon, and also gives the warlock player the chance, if this is a sidebar discussion, to involve the party to see what they make out of the shiny object leaning up against the wall that tastes metallic - limit the vocabulary to the scope of the spider's world awareness. This forces the player(s) to exercise their inner eye to interpret the imp's perception.
Besides being susceptible to different types of creatures, some of which could hunt by smell, the spider could be distracted by its ideal prey for example. It could even get lost or confused, and start sending back dis-oriented information. Or if you want to throw a real curve, let it get detected by something that can take control and manipulate what it sends back to the party, so they start the dungeon with a complete misconception and essentially walk into a trap to have to fight out of - that'll teach 'em.
To the larger question of party flow and involving everyone vs. just the warlock player, if it were me I would pass notes with the warlock player, or use a private chat on laptops or phones. This way the party could continue to take its own action with whatever information has been gained by that point, and the information received from the familiar is appropriately filtered through the warlock player for him to act upon however he wants (I have friends? that would let the party walk into an ambush for giggles). This slows the pace of information to track with the familiar moving through the dungeon and forces the warlock player to command the familiar to get results, while the party can proceed with their actions, and the warlock can update the party as information comes in.
It also, in a way, simulates the telepathic link between the warlock and the familiar via chat / note-passing - so no spoken words are ever used to describe what the familiar sees. This can serve to effectively differentiate it from spoken party communication, as well as potentially represent it as less efficient - an artistic choice, perhaps, but one which could condition the party and the player to take it less for granted. But it does make for a nice group dynamic: without any verbal or audible communication, all of a sudden the warlock player says "OK guys, now I'm getting back from my familiar it's in a room with lots of firelight and creatures making noises at each other. If I'm tracking it's position vs our position correctly, it should be maybe 2-3 rooms to the west".
This might require a little bit of juggling between speaking with the entire party and managing the private chat / note passing, but spacing out 'familiar reports' could also shift away from the 'pre-entering-dungeon' ritual of everyone else sitting and waiting for the imp to auto-map the dungeon, and forces the warlock to wait to get pieces of useful information instead of getting it all up front. Or if the party insists on waiting to enter the dungeon until the imp-mapping is done, it could get the party involved if they're helping to organize or interpret 'data' as it comes in 'real-time' over chat or note-passing to the warlock player.
In any case, I certainly wouldn't give the complete description of rooms via familiar to the warlock - I'd want to save something for when they actually enter the room. "The shadowy lumpy mass your familiar saw in the southwest corner turns out to be sacks of grains and fruit in various states of decay."
I suppose if you're going to take this kind of approach, you should give fair warning to the players. I can see a player protesting that their familiar should have seen something you didn't tell them about - better to remind them ahead of time that their familiar is limited by their senses / awareness, and that your discretion is ultimately motivated by wanting to create a compelling experience for everyone involved.
I should also add that I'm not current with specific rules, so if anything I've suggested contradicts any, apologies.