What are you using for SMS/MMS and email apps?
Using the native SMS/MMS app on my Moto G, and K9 Mail, I get both. Didn't have to do anything special. (Tho I blocked K9 Mail on the watch. I get way too much email--much of it spam.)
ETA: I also got notifications from Signal - Private Messaging, for the short time I had it installed.
Jim