I'm not familiar with that gel peel, but glycolic peels usually come in concentrations, like 15, 33, 50%, etc. The higher the percentage, the stronger the material. You can even get 100% unbuffered concentrations to mix on your own.
What should it do? Depends on your skin. The first peel, my results were similar to what you've described - redness and then nothing the next day. The 2nd peel a week later, and I got some red marks, flaking, and purging of impurities (zits). The 3rd peel, almost 2 weeks after that, and I actually saw frosting under my eyes within 2 minutes! (Not what I wanted because glycolic peels shouldn't frost like a TCA peel.) I am using emu and jojoba oil under the eyes to help moisturize and heal, but that area is going to scab up and peel, I can already tell. It will get uglier before it gets better. Anyway, my skin is tighter, firmer, and possibly smoother. It's only been 1 day since the 3rd peel, so results wont show right away. But I can surely tell I put something caustic on my skin. The average time I've left the peels on is 3 min.
If the product your using is strong enough to do what you intend, you should feel something by now.
It could be that the concentration is very low, or rather, too low for your skin to get to a peeling stage. I will tell you I've done 3 glycolic peels so far at 50%, approx. 1 week apart, and each consecutive peel was harsher and produced more results as I went. A lower concentration will still benefit your skin, but it might take longer to see results, or those results might not be as drastic. A stronger acid will show results quicker maybe, or more drastically, but the 'down time' is hard in that the skin peels and sheds in sheets instead of gradual exfoliation, and there's more pain involved.
Lactic acid, from what I've read, doesn't cause irritation and peeling. If your Skinseuticals has that, you may be improving skin but have no need to expect peeling or noticable exfoliation. Glycolic and salicylic is more likely to cause redness and peeling, and TCA - most definitely.
Check the ingredients and concentrations of those ingredients of the gel peel you have. You can always move up to a stronger peel though. The peels are affordable and last a long while too.