I think you were right the first time and second time.
We have more than 2 rules here for accents in Spanish.
Rule 1: A strong and a weak vowel together make one syllable.
Rule 2: Words ending in a consonant (not including n and s) are stressed on the last syllable.
Therefore because the verb continuar ends in a constant, the accent is on the last syllable 'ua' . Why the accent on the 'u' in present tense? I think this is where your last reply comes into play.
If there were no accent on the 'u', the whole sound would be different and the stress vowel would be on the 'i'. because of the rule of weak and strong vowels together make one vowel and of the rules of stressed vowels on next to last syllable .