Hello Tawdry firstly just to say it sounds like you and DP have done all the right things by being sensitive to you DSs needs, and basing your decision for DP to move in around them being OK with the idea. Given their ages, it was good to take their expressed opinion into account.
A conflict of loyalty is very common, but IME, it tends to happen or at least be triggered if the DC picks up any "bad vibes" from the other parent, in their case from their DF. Do you know if your exP is supportive of your new relationship or maybe a bit negative, which your DC is picking up on?
DP and I moved in together in Feb (after 5 years of a long distance relationship) and he has 50/50 residency of his DS. My DSS has been lovely from Day 1, basically he has the 'implied' endorsement of his DF so is cool about me asking him to do things etc, but it has been a struggle over the years because his mum is very negative especially as I have tried to be consistent throughout, like your DP, involved, caring and trying to be the best SP I can (she misreads that as me overstepping the mark 
I have noticed DSS does sometimes feel a conflict which I have resolved successfully by having a quiet word with DP and ensuring DP helps with the discipline side so it shares the burden. Often, I will pick up on things where discipline is needed that goes right over DPs head 
Having a united front is critical. The difficulty can be when residency swaps to the other parent and the DS gets mixed messages about "so-and-so isnt your DF/DM" which can make the child feel guilt and conflict. Not trying to make a problem where it doesnt exist but it may help explain things.
I think in your case, it is early days, as you mention things happened quickly. Thats OK but all I would say is that it took me several years to really build the trust and confidence with my DSS and I still have to work at it on a daily basis! In time, perhaps in the coming year, your DP will find things find their own level. Yes, DCs like to cherry-pick, they want the nice bits, but dont like the other bits and you are spot-on that they need to be prepared to take the whole package!
In the meantime, if you haven't done so already, maybe have a chat to DP about the matter of the ad-hoc pressie-giving, could that be something to hold off on, for the time being, or else any gifts could be joint from both of you, to take the focus from just being from DP. Over time, your DSs will get used to him being around and as they are now starting to think more maturely, they will see the logic when he mentions to them about homework etc (ie it doesnt have to be a conflict of loyalty for them to take on board your DPs comments).
I found with my DSS he is starting to tell the difference between how we "discipline" him nowadays, as he is a teenager, we arent telling him off like he is a little boy, we are giving him advice that he can accept or reject, he is too grown up for a telling off. A bit of reverse psychology works a treat sometimes!
I hope this helps!