Tight End illegal shift/ False Start

[Theisey]

First of all, try not use "no defensive player came offdside" as a criteria for determining whether team-A committed a false start.
That has no bearing.
The sole determination is whether you the official judged that the team-A player simulated the start of the play.

Secondly, the player cannot be an END and a BACK at the same time. If he really was an END and stepped forward, that very well could have been a missed snap count and therefore a false start.
If he really was a BACK, he still can commit a false start, but if his movment forward was slow and easy, all he was probably doing was to shift to a new position. Hopefully not making the formation illegal in the process.

Your final words make me think to know what to look for and either he did or didn't start the play is your judgement call.