No, timers are not transferred automatically. You need to export them from the old device and import them on the other device.
Here’s a video explaining how:
There are two apps Seconds and Seconds Pro. Both have the same features once paid for but they are not interchangeable. If you purchased Seconds Pro you will need to download that one again from the App Store:
If you bought the in-app purchase via the free app Seconds, then you will need to download that version again and upgrade in the app by tapping the upgrade notice then tapping Restore Purchases.