You may get DOMS, you may not. Likely it will decrease the more you acclimate to this type of training and eventually disappear. The idea of the program is to acclimate for 2 weeks and then push really hard for 2. Hopefully you will only be in record territory next week and the week after. The whole premise behind the program is that it pushes you right to the edge of overtraining (called overreaching), after you deload the body will recover and adapt. The problem is that everyone's tolerances are different as is their training history, what will allow me to train for 4 weeks and overreach might bury you and what someone else does might burry me.
This is why so many cookie cutter programs focus only on intenisty (%1RM) and just make a basic 'least common denominator' type volume base - volume massively effects the workload equation. This is even true among elite calibur lifters with same weightclass, experience, and maximum lifts - one guy might be able to handle a lot more volume than another, just a personal thing although obviously they are both putting up the same weights so it doesn't mean anything really except in program design.
So anyway, this is why I have the program set for 5x5 on one day and 1x5 on another day (for M/F), tell people to start very conservatively, match records on week 3, and exceed on week 4. This tends to really only load them up for maybe 7-10 days and be more tolerable. Maybe this is too much for you right now just due to genetics and training history. You could either start lighter next time and/or use 1x5 protocols on the M/F for some lifts and possible 1x5 for the dead or some such (you could do 1x5 for everything but that might be too little to put you in overreaching - a lot closer to the novice/intermediate program which is linear single factor and designed to be tolerated for longer periods). It's really a continuous scale, the other way transitioning to 5x5 on M/F and adjusting weight selection or adding volume beyond that.
Anyway, if performance hasn't dropped yet, you should be okay. If it drops 10-15% for more than an odd workout, you need to deload. Use this first run as a method of getting a good idea of your base tolerance and then work of that for your next program by adjusting if needed. If you are getting stronger and gaining weight, it's impossible to call that overtraining. Maybe just not used to this type of program but if strength and muscle are increasing - you aren't hitting the wall yet - even if they stall it's not the wall (but dropping is).
Hope that helps shed some light and gives you some ideas what to look for. Already being 2 weeks in and seemingly getting solid results it would be a shame to pull the plug at this point. At a minimum you'll have an excellent idea on whether or not the program needs adjustment. You might even find some of these symptoms disappear. BTW - make sure you use the 2x deload protocol, don't risk the 3x in the case that you are already having issues.