For part-time earnings, the first €75 euro of income above the SWA rate is disregarded, and 25% of the balance over €75 is also disregarded.
Assuming that the amount of BtoEd allowance paid is €188 euro, and earnings are €75 euro, the calculation is as follows:
total income = 263
SWA rate = 186 (single rate)
Income in excess = 77
As 75 euro of the income in excess is from part-time earnings, it attracts a full disregard.
The remaining 2 euro is considered income in excess and must be paid towards the rent.
The person must also pay the minimum contribution of €24 per week.
Provided his earnings are €75 euro or below, it shouldn't make any difference to his Rent Supplement. If earnings go over €75, then some of the earnings (75% of the amount over €75) will be considered income in excess and will have to be paid towards the rent.
Even if the additional income makes no difference to his Rent Supplement, he should still advise the CWO that he's started work.