When talk is about digital trigger systems this R&S appno is very good to read.
Of course different manufacturers do things bit different way and also in cheap scopes may simplify something but main principles stay. Also this appno is quite old in this special thing because data handling brute force overall is gone fast forward and down in price.
R&S:Benefits of digital trigger systemThere is also R&S paper what goes much more deep to inside digital trigger... but at this time just now I did not find it
Of course there is fast interpolation between true sample points... how perfect it is depends...
About aliasing. Of course ADC aliasing may smudge everything. Decimated samplerate aliasing is bit different. How anybody can even think that system know what is alias and what is true if only knowledge is data out from ADC.
This is why manufacturers need take seriously filtering before ADC. There is NO free lunches. It need do and it need do carefully. Now many manufacturers, specially B and C brands are careless and lazy just in this very important point. They build many kind of digital filters after ADC and think all are happy. Yes it is easy and so on but only right place is in analog pathway before ADC. Period.
Of course manufacturers can think that who cares if cheap scope is crap in this thing because users many time do not know anything but looks miracles and wonderful miraculous phenomena about electric signals on the screen and thats all. Siglent, Rigol, Hantek, Owon, whoever, / DO your homeworks and implement enough good filters to analog front end, even when some population may criticize this and are not happy because then they can not get amazing bandwidth. These are measuring and test equipments not entertainment systems or decorations. Many times best modification is reduce BW or modify front end BW shape to more steep and not try make it as wide as possible even when it looks like some kind of fashion when all want hack more MHz. More wide is not always best at all. ADC is frequency dowconverter...
If aliasing happen with decimated samplerate it may be different case with digital trigger engine because trigger can work before decimation always with ADC real running speed.
Digital trigger system have one obvious limit.
As the digital trigger uses the same digitized data as the acquisition unit it is important to note, that triggering only on signal events inside the ADC range is possible.
Conventional analog trigger engine do not have this limit!