There are no set rules. Weekly-paid workers typically work 'a week in hand', whereby they get paid at the end of 'Week 2' for the work they did in 'Week 1'. Similarly, some-monthly paid workers have to wait until the very end of their second month's employment before getting paid for the first one. So, as another employee has indicated to your OH, it's the employer's choice of 'cut-off date', together with how long they allow for processing data, that matters.
In some salaried occupations, such as teaching, it's common practice to pay staff in the middle of the current month that they're working. (When I started teaching for example, my contract commenced on 1st September but the school didn't open after the summer holidays until 8th September. As the local education authority paid staff in the middle of the current month, I only had to work for one week before receiving a full month's salary!). Others tend to pay their employees a week or two (or occasionally a full month) after a specific cut-off date. Some employers though will advance salary to recent starters who're experiencing cash-flow problems.