Many native speakers either don't know this rule or choose not to follow it.
Either that, or they use a different grammar book than you do.
Eg. Quirk* gives this example (p: 1065)
They liked our singing. (They liked our ‘mode’ (manner) of singing, the way we sang.) This has a nominal (noun) quality.
They liked us singing. (They liked the fact that we were singing – the ‘act’of singing.) This has a more verbal quality.
Quirk writes: "Traditionally this mixture of nominal and verbal characteristics in the -ing form has been given the name 'gerund'." (1291). The form that takes a genitive has a more nominal quality.
This allows the following example (mine) of a conversation in correct English between two women about B’s husband:
A: Do you like
his singing?
B: No,
his singing is awful. He can’t hold a tune at all.
A: Do you like
him singing?
B: I don’t mind
him singing in the bathroom, but I draw the line at
him singing in front of guests.
A: So you don’t like
his singing, but you don’t mind
him singing in the bathroom?
B: That’s right.
By this reckoning (and I agree with Quirk), the correct sentence for Alena is:
I hate them talking like this.
* Quirk, R. et al.
A Comprehensive Grammar of the English Language. Longman: Harlow, 1985.