If you don't think they're the kind of player to exploit it, you could just give them that initiative-triggered free action for free - with the catch that you reserve the right to change your mind at any time, depending on how things play out.
If you still want some kind of drawback to it, you could, say, adjust their particular features specifically. Something like:
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Until you gain the Instant Manifestation feature at 19th level, you cannot take the Manifest Eidolon action directly; you must perform it as a subordinate action, such as through Meld Into Eidolon. You gain the Rancor Manifestation action.
RANCOR MANIFESTATION [one-action]
[Emotion][Mental][Summoner][Unique]
Frequency until recharged (see below)
Requirements Your eidolon isn't manifested.
In a fit of rage, your shadowy rancor bursts from you immediately and without mercy. You Manifest your Eidolon. This near-immediate manifestation is much more strenuous than the typical manifestation, and your eidolon can only remain manifested for up to one minute, after which it unmanifests.
Once your eidolon has unmanifested, you can recharge your rancor as a two-action activity, which has the concentrate, emotion, and mental traits.
Special If you have the Instant Manifestation feature, you no longer need to recharge Rancor Manifestation, and your eidolon can remain manifested indefinitely.
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Modify this untested disaster as you see fit.