First of all, you really need to understand that Deutschlandsticket is only valid on local trains. They don't cover long distance trains no matter what.

The state of your arrival/departure doesn't matter, the operator of the train does. Normally this changes strictly at the border - for example, travelling to Czechia there is a "virtual" fare point at the border and you can use your Deutschlandsticket up until there and also buy a Czech domestic ticket from there. But there are exceptions, e.g. when going to Austria, operator of the train changes at a designated station so you can use Deutschlandticket all the way to Salzburg (on local trains), or Austrian fares all the way to Lindau, etc.​​​​​​