1. For public holiday falling on rest day (eg Sunday), the following day will be a public holiday as replacement. So, you will get a day's salary for working on Sunday and a replacement holiday the next. This is acceptable.
2. For public holiday falling on off day (eg Saturday), you should get a day\s salary working on your off day. If the management agrees to give you a replacement, that is also acceptable.
If you don't get paid anything for working on both days but get only a replacement, then I think you are at a disadvantage.