The ILM process checks the indices to see if they match any action on an scheduled interval, per default this interval is 10 minutes.
The maximum age is based on the index creation, so if you have a maximum age of 1 day, it will check your indices to see if they were created more than 24 hours before, if an index matchs this check, it will be rolled over.
Since it can take at least 10 minutes to apply the action, the behavior you describes seems to be normal and expected.
ILM works better with bigger intervals, if you want daily indices ILM is not the best option.
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