What happens when the stealth check is failed
First lets look at the rules of surprise.
Surprise (Starter Set Rulebook 9)
The DM determines who might be surprised. If neither side tries to be
stealthy, they automatically notice each other. Otherwise, the DM
compares the Dexterity (Stealth) checks of anyone hiding with the
passive Wisdom (Perception) score of each creature on the opposing
side. Any character or monster that doesn't notice a threat is
surprised at the start of the encounter.
If you're surprised, you can't move or take an action on your first
turn of the combat, and you can't take a reaction until that turn
ends. A member of a group can be surprised even if the other members
So, since Glasstaff notices a threat (as represented by his Passive Perception being high enough), he is not surprised at the start of the encounter.
All that really means according to the rules is that he has his movement, action, and reaction available to him once combat start.
Now, the adventure book does give some specific guidance on what should happen if he is aware of the PCs coming for him. However, the guidance is just if they come through is workshop first, where his familiar notices and alerts him. It doesn't say anything about the PCs coming down the secret passage.
So does he try to escape or not?
He does what makes sense to you, the DM.
Adventures (Basic Rules 5)
An adventure might be created by the
Dungeon Master or purchased off the shelf, tweaked and modified to
suit the DM’s needs and desires.
The adventure book is not a rulebook, it is a guide to help the DM create an enjoyable experience for everyone. I couldn't find a clear reference in the Starter Set books for this fact, but I did find the above in the Basic Rules PDF.
You are expected to tweak and modify the outline provided in the adventure book. So don't feel like the adventure book is a strict outline of what must happen, or that it contains all the information you need for any situation. I'm not sure if you felt it had to be followed strictly, but just in case, I wanted to address that.
Ok ok, so what should happen?
Narratively, Glasstaff knows something is in the secret passage. Maybe he thinks it is a Redbrand, and so will just go check out why one of them is bumbling around outside his study. Maybe the PCs actions previously (in town and the Mansion) were enough to put him on guard, and he decides that it may be them and he should make a run for it now.
When my group (that I DM'd for) played, they also went through the secret passage. They did manage to surprise him, but once he was able to move, he immediately made a dash for his workshop. Why? Because he wanted to escape and towards his workshop was now the most clear path of escape.
If your players fail their stealth checks, I would consider having Glasstaff immediately try to make his escape out through his workshop, if he has some reason to believe that what he heard in the secret passage is a threat to him. I would have the players roll initiative immediately after the stealth check fails, and have him start moving while they decide if they are going to rush forward or try to keep quiet.
Of course, if he has no reason to believe the PCs are in the mansion, he may not think it is a threat, and so may use his turn to open the secret door and look.
Roleplaying Iarno (Lost Mine of Phandelver 26)
Iarno is just as thuggish and arrogant as any Redbrand outlaws.
Keep in mind, someone who is thuggish and arrogant is not likely to run just because he heard a noise. He will likely want to confirm the threat in some way, or at least prepare himself for battle, by getting away from the secret door and near the workshop door, ready to start slinging spells.
Surprise is not automatic just because the adventure book (that you are expected to tweak and modify) says someone can be surprised.
Surprise (Starter Set Rulebook 9)
If neither side tries to be stealthy, they automatically notice each
If the PCs just barge down the stairs, they are not trying to be stealthy, and so Glasstaff automatically notices them. Simple as that. That also covers the situation you mention in a comment, for the Common Room, where the players bursting into the room means no surprise for anyone, since the Redbrands certainly weren't trying to be stealthy. So that situation is just repeating what the rules on surprise say.