I's always assumed that you shouldn't notch the bottom for the same reason but a spot of googling reveals loads of information stating that it's okay as long as you don't notch top and bottom at the same end.
Therefore lies a problem. If the joists are notched on the underside and hidden out of view from the room above, any installers lifting the floor boards above are not going to be aware that the joists have been notched on the underside if the notch can't be seen. The joists might then be notched in error on top
and bottom.
I've nothing against plastic, (although I only use copper,as that's my preference) except that for changes in direction, a fitting is generally required. Multiple changes in direction means multiple use of fittings and they are big, bulky and unsightly if on view. For peace of mind in areas that are inaccessible, I personally feel safer with soldered fittings.
The vast majority of new builds use plastic systems now and I don't see this trend changing anytime soon. It's easy to slag off plastic like in this instance, because it does look unsightly at times and the fittings are big, ugly and bulky.
As to the OP, I'd perhaps say without any malice intended to either yourself or the plumber involved, that the job looks like there was either a misunderstanding or breakdown in communications between you both. I'd suggest that you ask for the pipework to be pressure tested (as per manufacturers specs.) before the ceiling goes back up and perhaps meet him him half way with the way that the ceiling can be fitted to accommodate his pipework.
Whatever you decide, the pipework MUST be pressure tested first anyway.