Backwash line - softener and sediment

[AdamC]

I need to tie a sediment filter backwash line into my existing softener discharge line. Planning to use a simple Y or T connector. I assume valves in the control heads of both the softener and sediment filters (both Fleck 2510) would prevent backwash from entering, and therefore negate the need for check valves. Is that correct?

Thanks!
Adam