eAPIS is not necessarily the only requirement and some airports, KTEB for example, have their own jobs worths, sorry, officers who require you to secure approval before you land.
For KMIA, why not get the answer from them direct rather than via a trip support company who assumes they know what they are talking about.
Miami customs: +1 305 526 7155
Works every time for me, regardless of the airport.
If you would like help submitting eAPIS, in and out of KMIA, let me know.
On TSA, check the latest NOTAM for requirements - FDC 0/6432 is the reference.
Hope that helps.