No. Roth conversions are disregarded with respect to the one-rollover-per-12-months rule.
You would expect to receive only one Form 1099-R reporting the conversion unless you had taxes withheld and you were under age 59½ at the time of the distribution from the traditional IRA. If you were under age 59½, the portion that was converted to Roth should appear on a code 2 Form 1099-R and the amount(s) withheld for taxes should appear on a code 1 Form 1099-R.
