There is one Ecobee DTH that supports non-Ecobee sensors - it’s the one you’ll find that costs money. To my knowledge, none of the free DTH for Ecobee support non-Ecobee sensors.
If you use the SmartThings DTH and the temperature settings in each of the Routines, you don’t need any additional SmartApps.
Alternately, if you would like SmartThings Mode changes (Home, Away, Night) to change the thermostat Program (aka Climate), then yes, you’ll need some SmartApp (or WebCoRE) assistance. The free Ecobee Suite I maintain includes the necessary SmartApps to change Thermostat Programs based on Mode Changes or Routines being run. You can find it here: [RELEASE] Free Ecobee Suite, Version 1.2.*