it is quite simple,\
You have a 1 second timer, that causes an interrupt every 1 second.
Your other times are multiples of that 1 second.
So, at the start of your program set a 10second counter to 0 and set a 1minute counter to 0.
At each 1 second interrupt, increment both counters.
Each time the 10 second counter steps from 9 to 10
- reset that counter to 0
- process the 10 second activity
Each time the 1 minute counter steps from 59 to 60
- reset that counter to 0
- process the 1 minute activity