The first thing to do is not to panic! When an incubator begins opening, the contents are added to your account. Meaning even if you did not get a chance to see the full incubator opening animation, the contents are still added. If you reboot the app after getting disconnected during an incubator opening, you should be met with a recap screen that displays what the incubator contents held:
If you did not see a recap screen, our best recommendation to verify received incubator contents is to note your Dart, Coin and Cash balance before opening an incubator and then note any changes made to them after the incubator was opened.

If you notice an increase for any of your resources, it means the incubator was successfully opened and any creature DNA that was included was successfully added as well (it's not possible for an incubator to reward resources without including DNA with it). You might even notice one of your creatures now has enough DNA to evolve!

If you do not immediately notice any changes to your resources after opening an incubator, try rebooting the app completely and double-check again to see if any of them increased.