Scheduling rollouts of new pricing can be done by modifying the effective date of a `tier.subscribe()` call. So you could do something like `tier.subscribe('org:' + customerID, 'plan:whatever@123', someFutureDate)`.
For communicating it to customers, yeah, you'll probably want to tell them their price is going to change ;) It might even be good to have an email campaign where they can check out the new price and decide to upgrade/downgrade/whatever with some time to make a decision. Customers usually don't love being forced into things without notice. Tier doesn't handle this part of it for you, but it does give you the tools to make the actual subscription change pretty easily.
[1] "Mostly" immutable. You can of course go into your Stripe account and edit anything they let you. But Tier makes it easier to just add new plans and leave the old ones there.