Depending on the size of the database and the operations and transactions is doing a the time of the change of tier, the scale up/down of the service tier may range from a couple of minutes to a little more than one hour. For example, 750 GB database may usually take 30 minutes of "downtime" until the change of tier is completed.
Transactions opened at the time the change of tier is started, they will be rolled back, and logins will be disconnected. Contained database users will stay connected.
Query plans may vary after scaling up/down because the number of threads available for query changes, and the data cache and query cache will be cleared.