I found information online (sorry can't quote a particular source atm) but found it in many places..... at least for humans, it is contraindicated (meaning bad to do) to rub or massage the insulin injection site... both for the reason you discovered, that the insulin can leak out of the fresh hole you've just made, and also because you're disturbing the 'cell' of insulin which may cause it to be absorbed more quickly.
ETA: What I do is give him a good brisk (short) massage on the area BEFORE I shoot, Frog seems more comfortable with the injection when I do that.