No, a rollover doesn't count as a contribution.
401K rollovers are reported as distributions, even when they are rolled over into another eligible retirement account. An eligible rollover of your 401K funds to an IRA is a non-taxable transaction. Rollover distributions are exempt from tax when you place the funds in another IRA account within 60 days from the date of distribution.
Regarding rolling 401K into IRA, you should receive a Form 1099-R reporting your 401K distribution. Regarding reporting 401K rollover into IRA, how you report it to the IRS depends on the type of rollover.
If this was a direct rollover, it should be coded G. Enter the amount from your 1099-R, Box 1 on Form 1040, Line 16a. Enter the taxable amount from Box 2a on Line 16b. The Box 2a amount should be 0 for direct rollovers.
[Edited 02/09/2021 | 9:10 AM PST]
