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to come at just the right time
A fixed expression meaning that someone or something appears or happens at exactly the right, suitable moment.
Dein Angebot, mir beim Umzug zu helfen, kommt wie gerufen!
Your offer to help me move comes at just the right time!
'Gekommen' is the past participle of the verb 'kommen' (to come). In these fixed expressions, it is not used to form the perfect tense, but is part of an idiomatic expression.
Er ist gestern spät nach Hause gekommen. (Perfekt)
He came home late yesterday. (Perfect tense)
In the expression 'wie gerufen kommen' (to come at just the right time), the person for whom something is suitable can be in the dative. The subject of the sentence is the thing or person that appears at the right time.
Der Kaffee, den du mitbringst, kommt mir gerade wie gerufen.
The coffee you're bringing comes at just the right time for me.
The idiom 'gekommen, um zu bleiben' (here to stay) has a fixed structure with an 'um ... zu' infinitive construction. It is used to say that a new trend or development has become established.
Das Homeoffice ist für viele Firmen nicht nur eine Notlösung, es ist gekommen, um zu bleiben.
For many companies, working from home is not just an emergency solution; it is here to stay.
in time / on time
'rechtzeitig' and 'wie gerufen gekommen' both have to do with a suitable moment. 'rechtzeitig' says in a neutral way that something happens early enough for it to still work out. The expression 'wie gerufen kommen' emphasizes more strongly that someone or something appears at exactly the right moment and is very helpful. It is often used when a situation suddenly gets better. The words are therefore not simply interchangeable: 'rechtzeitig' fits appointments and deadlines, while 'wie gerufen gekommen' fits help or a lucky moment.
Du bist mit dem Werkzeug wie gerufen gekommen.
You came with the tools at just the right time.
Die Fahrerin bremst rechtzeitig vor der roten Ampel.
The driver brakes in time before the red light.