Multifinish is fine, I use it myself in Bathrooms and it's far easier to use than one coat plaster.

You wont like this but plaster should be left for 6 weeks before tiling!! A load of crap I know but thats what the tile adhesive manufacturers recommend.

I would personally leave it to lighten before you tile. Should take a couple of days in this heat.

As for preparing the plaster before you tile I would check with your adhesive manufacturer. They would normally recommend a particular primer. For example if you're using bal adhesives then use Bal Prime APD undiluted.