This answer takes the OP's assertion that Tzim-Sha had no good reason to speak English at face value and attempts to explain it without a frame challenge.
In the ninth Doctor episode The End of the World The Doctor described the translation matrix as a "gift of the Tardis, a telepathic field that gets inside your brain — translates".
If it is a gift this suggests that the translation ability could be passed to you, so the Tardis wouldn't have to be present for you to have the ability once you have travelled in it and received that "gift". That it is described as a field even inside your brain suggests that it still has a range.
In fact, think of this - when The Doctor, a companion, and another alien species are having a conversation, which language are they actually speaking? Does the alien speak their own language and The Doctor reply in English? If so, were the companion to speak to the alien and then in turn to The Doctor, do they seamlessly switch from speaking one language to the other? If the answer is that they all physically speak their own language but hear other languages as if they were their own, this means that the alien in these scenarios is also able to hear a translation. This would prove that the translation matrix has a "range" from the person with the gift. If it worked for everybody in the range of the Tardis indiscriminately then everybody in the area during every Earth adventure would notice they can now understand every known language.
Now, in this episode only The Doctor had travelled in the Tardis, so to discount the possibility that Tzim-Sha could actually speak English we have to explain away the individual spoken encounters he had with humans.
Rahul asks Tzim-Sha "where's my sister" and Tzim-Sha responds "ask me again". Rahul does ask the same question again. If you don't want to accept they are speaking the same language you could reason that Tzim-Sha didn't know what Rahul asked him. He may have imagined Rahul was begging for his own life, in which case he would have likely responded the same way. Likewise, if Rahul did not understand Tzim-Sha's response the chances are he would have repeated his question anyway because that is what he wanted from him.
The kebab man makes a number of comments to Tzim-Sha but he says nothing back.
The Doctor converses with Tzim-Sha at length but the others do show that they understand both sides of the conversation - for example Ryan directly responds to Tzim-Sha over the issue of access being granted to Earth. The telepathic field inside The Doctor's brain must have covered the others in this encounter.
Again, Karl demonstrates that he understands Tzim-Sha by responding when he calls him insignificant. But as in the last scene, The Doctor is present.
I have also been asked in comments why, if Tzim-Sha did not speak English, did he appear to speak English words. To put that a different way, why do we the viewers see all aliens/foreigners lips moving in synch with their spoken English words? If their words are being translated, shouldn't they look like they have been dubbed?
The Out-of-Universe explanation is obvious - it would be a production nightmare and not as enjoyable to watch. This is probably why just about every alien race in Star Trek speaks English, with the exception of the Klingons (but maybe they'd try harder to learn English if nerds stopped bothering to learn Klingon?)
As a viewer, we have to imagine that everybody is speaking their own language - that aliens are speaking alien, and the Romans in Fires of Pompeii are all speaking Latin - but that we are hearing English thanks to the Tardis translation matrix. And of course, as it is a telepathic matrix, perhaps that is why we (if you imagine that as viewers we are under it's influence too) also see that they are speaking it, or at least they appear to be.