Why wouldn't the sequester trigger federal pay cuts instead of layoffs?

That actually depends on how the agency being hit with the sequester chooses to deal with the cuts. They in theory could cut pay to workers, however many workers including the TSA are unionised which as a result mandates how much their workers get paid there by eliminating pay cuts as a possible outcome.

However, it is possible and not unlikely that the union/agency could reopen contract negotiations to make pay package adjustments to help compensate for the sequester. Granted they might not be willing to cut the full sequester percentage in pay and benefits but they might take some pay and benefit cuts in order to keep job losses to a minimum. It would however be upto the Union and Agency being effected to persue these measures and if ether party doesn't want to negotiate them then job losses will occur, unless cuts to other items can be made

I'm a federal employee.

If we get furlough, we will lose one day a week pay.

So, a 20% pay cut for 22 weeks.

This is on top of not getting a raise in 4 years.