If your 3 day ticket is a hopper - or at least good for any park, then ignore everything I'm going to say. It will be no issue.
We had an experience getting our FPs a bit more than a week ago based on something similar.
5 of us had a five day hopper. 2 of us had a 4 day hopper left over from a prior trip, and 1 one day (non-MK) ticket.
Things were going very well at 6AM Central time, until we tried to get the FPs for our first MK day. We were not able to get any for the 2 that had that situation. We could only assume that the system was applying the one-day ticket to them for that day, and since it wasn't good at MK, it wouldn't give them a FP.
I had to call (hold time < 10 minutes) and the CM had to escalate. It got worked out, and he stayed on the line to assure we were OK.
We missed out on some FPs for that day at MK, but we got a lot of hard-to-get ones at the other parks so overall we were satisfied (and we've since made several adjustments as passes became available as people are also adjusting their plans in subsequent days)
I'm really not sure if anything could have been done ahead of time. I realize what made this unique was the one day not being good at MK (we will prioritize that when we get there for our first park visit on arrival - Epcot).