Outlet Change with 4 Hot Wires
Critical issues here : 


Side tab cut, not broken off. That is not safe as the 240V between them could easily arc, illegal per NEC 110.3 as the receptacle's instructions say to break off the tab entirely, not cut it. This defeats the safety testing done by UL since UL did not test it that way. 
Backstabs are not compatible with 12AWG wire, the wire size now required in kitchens. 
Bending the wires onto the screws is very shabbily done (poor conductivity, and NEC 110.12). 
Backstabs and screws both in use (I believe that's not allowed).
Two separate circuits feeding the same yoke, but they are not handle-tied for common maintenance shut-off. (Alternatively, a 2-pole breaker can be used to accomplish the handle-tie, but never a double-stuff/duplex/2-in-1-space type.)
Neutral must be pigtailed - correct. This is so a receptacle can be removed without severing neutral for the other circuit.  


The fix is what you did: pigtail the hots and use screws only.  Do that on the other receptacles... or, switch to the $3 Leviton screw-to-clamp type, which support 2 wires under each screw. And break the tabs off properly, they have break lines, a few flexes should do it. 

When you are able, put the 2 circuits on a 2-pole breaker or handle-tie them.