There are approved methods to install tile over plywood, but the method you depict is not an approved one. If you want to use plywood, and not use some other decoupling layer, you have to have two layers of ply then use a pretty expensive highly modified thinset. the second one can be 3/8" and should not have a side lower than 'C' (i.e., D allows voids which are death to tile). Over a single layer of ply (assuming ceramic tile and not natural stone), you could install cement board, or use a decoupling membrane such as Ditra from www.schluter.com to minimize the buildup. check out www.johnbridge.com for more help on tiling.
With the 2/4's in contact with the concrete, if moisture is a potential problem, you should use KDAT 2x4 (kiln dried after treatment) pressure treated wood. The subflooring should be 'normal', though. "Normal" treated wood is still VERY wet, and will often warp or twist when it eventually dries out. If the floor isn't flat, you may need to do some extra work to get the sleepers to be fully supported and not rock while keeping the floor nice and level and flat.
An alternative for those tiled areas would be to use deck mud - this would level the floor and give a great surface to support the tile. It's probably cheaper than buying the wood and then you wouldn't have any issues with the wood and moisture. Deck mud is mostly sand (that's why it's cheap) with a little portland cement to hold it together. It gets packed and screeded down like damp beach sand - it doesn't flow.