punctually vs on time

punctually is not an adjective while on time is an adjective.

Word	Noun	Adjective	Verb	Adverb
punctually	No	No	No	Yes
on time	No	Yes	No	Yes

As adverbs, punctually and on time are synonyms defined as:

punctually (adjective)	on time (adjective)
	acting or arriving or performed exactly at the time appointed
	payable in installments within a designated period of time

punctually (adverb)	on time (adverb)
at the expected or proper time	at the expected or proper time