There is a wire coming from the amp that is the remote turn on wire, so it will turn on when I start the engine.

That is an incorrect statement.

Assuming a standard aftermarket amplifier... The remote turn on wire for the amplifier is not there for when you start the engine. It is there for when you turn on the stereo. Subtly different, but important.

Where should I connect this wire to?

The amp remote wire on your stereo.

But why couldn't I put it on the Ingition sense wire?

Because if you put it on the ignition wire, you will get speaker-damaging "pops" at inopportune times.

You would also be unable to use the "wake from standby mode" feature of the empeg.