All Scag machines that have pumps and wheel motors up to and including the latest models are recommended to use 20W50 motor oil, no reference to 20W50 full synthetic or synthetic blend is made in any of the Scag operators manuals for these machines.
On most of the Scag machines that have unit hydrostatic drive units, full synthetic oil is recommended per the Scag operators manuals for these machines.
Your Tiger cub has pumps and wheel motors.
With a hyd filter change, about 2.5 Qts of the total of about 4-5 Qts will drain out.
Should you decide to use full synthetic oil, you would still have the effect of a synthetic blend in the hyd system.
It would take about 4-5 oil changes to have as close to the affect of full synthetic as possible.
When you do change the hyd oil, when the hyd filter is removed, all the oil in the hyd reservoir will drain out, about 2.5 Qts plus what is in the filter.
As the filter is vertically mounted, fill the new filter with oil until it is full and no air bubbles are escaping, then install it. Fill the hyd reservoir with two Qts and let the machine sit for at least 1/2 hour or more. This will allow the system and filter to purge out most of the remaining trapped air. Start and run the machine with the levers out, then operate the machine normally. Recheck the hyd reservoir oil level and top off if needed.
Just did my Tiger Cub as I also replaced the L/H hyd pump, drive belt and idler/tensioner pulleys although the pulleys were OK.