A rollover from one Roth IRA account to another (or to the same one) doesn't change anything about the nature of the funds for withdrawal -- contributions are still contributions, earnings are still earnings. (In fact, all Roth IRA accounts are aggregated, so there is no distinction between accounts anyway. A rollover from Roth IRA to Roth IRA is as if nothing happened at all.)
The source of your confusion is probably from reading the ordering rules for Roth IRA withdrawals in Publication 590-B. It is 1) regular contributions, 2) conversions and rollover contributions, and 3) earnings. You might have thought that these "rollover contributions" include rollovers from Roth IRA to Roth IRA. However, in the preceding paragraph, they were talking about "rollover contributions from qualified retirement plans" (i.e. rollovers from Traditional 401(k), which I would probably call a "conversion" since it goes from Traditional to Roth, but they call it a "rollover"). And in the following paragraph, it explicitly says:
Disregard rollover contributions from other Roth IRAs for this purpose.