The situation to which I think you refer is covered in the AGB (Conditions of Carriage) for the Bahn. It is specifically called Vor- und Nach-lauf and says, in German, that for Sparpreis tickets, only the train(s) of the Bahn (long distance train: ICE, IC, or EC) are specific to that ticket. Any regional train (the S-Bahn is a regional train) with the same route as the ticketed regional train can be taken to get to and from the specified train on the day of validity until 10:00 the following day.
Beförderungsbedingungen für Personen durch die Unternehmen der Deutsche Bahn AG (BB Personenverkehr), § 3.3.1.2
I believe your ticket also has some wording saying, in German, the same thing.
If your ticket starts from the Munich airport and goes through München Ost to Italy, it has to include an S-Bahn from the airport to Ost and your Bahn train from there is an EC (not an ICE) via Rosenheim, Innsbruck, and Brennero. The departure board for the Munich airport shows only a few regional trains (NV) to Regensburg and the S-1 and S-8 into Munich. The departure board from München Ost shows only a few ICEs, those going to either Austria or Frankfurt.
At the airport, the departure schedule will show the S-1 going to Ost and the S-8 going to one of several station, Herrsching being one of them. Those are the end stations for those train. The S-1 goes around the west side of town, through the Hbf, and terminates at München Ost, but takes longer to get to Ost than does the S-8. The S-8 goes around the east side of town, stops München Ost, then at the Hbf, then terminates in one of the towns to the SW of Munich near Ondechs. Take the S-8 even though the S-1 says München Ost.