This is my first time GMing. I am unsure as to whether the fellow escapee NPCs could be leveling up with the PCs. I do not see any rules for it, but it doesn't make a great deal of sense for them not to if they are participating in defense, etc.
T.J.L.'s answer pretty much sums up the RAW on the question: NPCs, if they have participated in combat, will get an equal share of experience. That is the general rule. What this also means is, for non-combatant NPCs like Stool and Shuushar (both of whom I like to send to the back, where they won't take up 'camera' space), when they have absolutely no participation, get no experience.
On the NPCs leveling up, they do not have character levels, so they wouldn't. It is also ill-advised to give them or increase their potency with XP gain, since, especially early on, some NPCs simply outgun the typical 1st-level PCs (Jimjar, Eldeth and Derendil are particularly strong!). This would result in PCs lagging behind as the NPCs statblock 'levels up' at the same rate as the PCs level up. Remember, the PCs are the stars! And by 4th-5th level, they will start to feel a lot stronger than their NPC friends.
However, I have run Out of the Abyss without sharing experience with the NPCs, and it seems to work out fine. We're nearing the close of the first half of the adventure (Blingdenstone still unexplored), and the characters are at 5th-level.
Chapter 7 mentions that:
The characters should be 8th-level by the start of [chapter 8]. If they're not there yet, plan additional encounters so that the characters can earn more experience points during
their overland journey to Gauntlgrym
To me, and observing the pace at which they are leveling up with XP divided among NPCs, this note sounded very odd. I didn't want to throw-in unrelated "fillers" to bridge the level gap, dividing XP with all the NPC party members exacerbated this, so I forewent it in favor of a better paced story.
TL;DR Yes, NPCs get a share of XP as a general rule, but in this module's case, it is not needed.
Any NPC that accompanies the adventurers acts as a party member and earns a full share of experience points. When determining the difficulty of a combat encounter (see chapter 3), make sure to include all NPC party members. - DMG, p.92
The quote pretty much says it all - NPCs in the party suck up a share of the XP.
However, NPCs are not built the same way as player characters. Even if they are of the same race a player character can select, even if they have added class levels, they're a monster1. They don't have a method of advancement - that's for player characters - they just consume resources.
1If you have built it as a player character, you have what's known as a GMPC, a Game Master Player Character, not an NPC. You can search around the stack for questions about the perils of doing so.