It makes sense ecologically to combine dumpster trash on construction sites. Quite frankly, this is done all the time in small increments. Many times it's done somewhat clandestinely and isn't noticed.
On a remodel I designed and managed about 12 years ago, we needed a container and a half of haulaways.
In this case, my client was a friend, but the contractor wasn't. He didn't take advantage of the situation, he asked me if it was okay to put in some rubbish from another job site he was working on. We agreed that he would show me the amount he was putting in and if by chance we went over the 2 dumpster estimate, he would pay for the third one.
You have to pay for a dumpster whether it's filled up or not. Better to make your contractor happy and not get too picky about things like he should pay half or he should pay a quarter, etc. Some folks can become passive aggressive, although you would hope not, but he could always cut corners in ways you don't know if he decides that he doesn't appreciate your attitude, friend or not.
I would just call to his attention right now when he's done it, how much you observe being in there and if your disposables don't fit in this dumpster, you would expect him to handle the next one. AND that is assuming that the excess amount you need does not exceed the amount of space he used up. Also ask him not to place any more of his materials in there without discussing it with you first. Just tell him nicely that you want to have the opportunity to observe the amount.