Tiagra 9 speed triple front with a 10 speed group
Yes, it will work, but you need to double check shifting range settings — stops — on the front derailleur.

I recommend use second and third positions of shifter for inner and outer rings respectively (not the first and second).

If you will use not only triple front shifter but also a triple front derailleur you must consider that shifting on double crankset with triple derailleur wouldn't be as fine as with double derailleur (because of triple derailleur frame form).