With regard to your question about "punctual" and "punctually', the usual
rules apply: if you're modifying a noun, use the adjective: "a punctual
employee"; if you're modifying a verb, use the adverb: "They arrived
punctually."; as the complement to the verb "be", use the adjective: "I was
punctual for the seminar." - compare - "I arrived punctually for the
seminar." If you're paraphrasing "be on time", you're using "be", so the
adjective is used: "She was never on time." = "She was never punctual." Hope
this answers your query.