Help with 2 Dimmer Switches and bad wiring
Almost certainly the hot is one of the 3, and the single wire goes to the light this dimmer controls, while the other 2 wires feed unswitched hot to other devices. Given that your assumption is opposite, you MIGHT want to consider an electrician, or further self-education.

See Light Switch Terminals which is a very similar question (one less wire in the bundle.) "Braiding 3 together" is wrong. Using a wire nut (or other listed splice mechanism) to join 4, with the 4th being an additional short "pigtail" to connect to the switch terminal is correct.

Incidentally, having 3 wires stuck in one pole does not make the switch a 3-way switch. A 3-way switch is a particular type of switch commonly used so that you can control lights from two switch locations, which has 3 separate terminals rather than the usual 2.