Really? No, it's just a normal "T" sound...
Actually, there are two different "T" sounds in this word! Although the letter is the same, from our point of view consonants can be "soft" and "hard". The one followed by "i" becomes soft.
When you say the hard т (as in та то ту те ти) you touch your teeth with the tip of your tongue (you can even make it stick out a bit as in "th" for an exaggerated effect), and for the soft т (as in ті тя тє тю ть) you press your tongue against the roof of your mouth.
Maybe it's the soft "т" that sounded like "к" for you?
Not at all. "Toma" - it's a female name. You can see it, because there is "aunt Toma", not "unсle". The full name is Tamara, it's not so popular slavic female name with semitic origin (from name of Tamar, a jewish woman, a personage from the Book of Genesis)
And the short nickname of Artyom sounds like Tyoma (or Töma) - and there is very strong difference between two names "Toma" and "Tyoma" - because you can't just call male by female name and vice versa.