Mazda2 excessive vibration on cold start

So, did replacing the RHS mount solve this issue? I have the exact same on my 2012 Mazda2. It's very rough (my wife says 'growl-ly') on (i.e., when we leave the house or leave after work), but it's normal after 3-5 minutes of driving, or if we are running errands in-between stops. I'm wondering if I have the same problem with the same solution.
Replacing the RHS motor mount seems to have fixed excessive vibration from start up, and especially while idling in drive.