The thing is: there isn't a hardcoded "Round 2 intro". The way you do this is by changing the state 5900.
If you take a look at your common1.cns, you will see this:
;---------------------------------------------------------------------------
; Initialize (at the start of the round)
[Statedef 5900]
type = S
[State 5900, 1] ;Clear all int variables
type = VarRangeSet
trigger1 = roundsexisted = 0
value = 0
[State 5900, 2] ;Clear all float variables
type = VarRangeSet
trigger1 = roundsexisted = 0
fvalue = 0
That state happens before any round, so this is why there is a code to reset the variables.
Take a look at your state 5900 - remember that if you can override states in Mugen, so if your char has a state 5900 in any .cns file, Mugen will read it instead of the common1.cns under data folder - and see if there is any animation change.
In RMM Pharaoh Man, for example, I use an animation between the rounds, so its a simple changeanim:
[State 0, ChangeAnim]
type = ChangeAnim
trigger1 = !time
value = 5900
persistent = 0
You can do some cool things there. For example, in the next RMM build, Quint will execute a custom animation during that state if he loses the first round - because he dies on the first round and travel back in time for the second round.