When you mark a job as "Done" on the worksheet, either on the PC/Mac or mobile app, it will default to today's date yes (as determined by the system clock).
If you're marking it as done retrospectively (e.g. you did the job a couple of days ago) you can click the calendar and change the "Done" date.
The due date is entirely separate. You can change this yes, but generally you'll leave it to CP to work out when the job is next due based on it's schedule (e.g. 4/8/12 weekly).
As Soupy pointed out, there is a setting: "Schedule Next Due From" which you can either set to "Date Actually Done" or "Date Originally Due" if you want to keep the job on schedule even if you did it late.