The Vita Appears to be able to connect correctly to the PS4. The message pops up saying that it is turning the system on, but it never happens. If i turn the PS4 on in advance it works, but turning it on remotely doesn’t work. This is a common scenario when attempting to turn the console on.
This can be caused by a setting on the PS4. In the settings menu there will be a category for Remote Play. Go into this and make sure that the system stays connected to the internet when in standby mode. This will unlock an option to allow the system to be powered on remotely. This should solve any issues of starting it up remotely.