If a DPS has a combat rezz, they should be priority over healers to use it, but they should NOT use it without being asked.
There are plenty of times you might not want to automatically burn your battle rezz (e.g. opportunity in near future to execute combat stealth + rezz).
Yes, they should, however they should of course also use their head and realize that sometimes it's better to not use it yet. That's rare though.