Once the push part of the task has finished for ALL machines, then it will become a policy for the failed ones.
If you are on 8.7, the client machine will run the policy again when amclient.exe runs and checks in with the core.
If you are on 8.8, the client machine will run the policy when policy.sync.exe runs.
Either way, if you are using default settings, that will run once per day for each client. The time of day will be random and vary by client. So it should be spread out.