If your people giving you references are good, then that will not have any baring. I had a similar thing when I started my career. Got offered 2 more that i'd applied for at the same time. This one came through first and the basic course was into it's 3rd week when Igot the offers. I spoke to someone in confidence, and the first couple of years were suddenly a lot harder for me than others. Maybe testing commitment or what ever...
I guess with hind sight, I would still be honest, but would not offer anything up unless specifically asked.
You have already shown your desire to suceed with one by giving up another. So long as the offer of your preferred is solid. The old adage of 'a bird in hand is better than 2 in a bush'...
All the best
Mr. P