Generally we would say the same in Welsh and later on the patterns for 'I cleaned Tuesday' etc are introduced. However the 'dw i wedi' sentence is very straightforward, follows the other forms in the initial units and is an easy way of expressing an action in the past.
Could you use sentences that would make sense when teaching this form of the past tense? I know it's been mentioned before, but if Welsh people wouldn't say "Tuesday I have cleaned", could you change the sentence to "Today I have cleaned", "I have cleaned this morning", "I have cleaned tonight". That would be much more useful.