I think there is no a t sound. In the Czech language, it is written český and Čad, a letter č is pronounced just the same as a ch letter in a word cheese. Check the pronunciation of words Czech, čeština or český and a word צ'כית here. The first letter sounds just the same. https://translate.google.cz/#view=home&op=translate&sl=en&tl=cs&text=Czech
Well, I think that the <č> in český and the in cheese and the <צ'> in צ'כית are all pronounced [t͡ʃ]. Of course the tip of the tongue contacting the alveolar rigde transitions with friction so fast backwards that it is perceived as just one sound, but the starting point is nonetheless there, where you would produce the voiceless plosive [t]. But phonetically you are right of course, because the air is not released with a sudden explosive force.
Well, whether a pair of phonemes can form a new single phoneme, in this case an affricate, was the question here. It is often difficult to decide if a stop and fricative form a single phoneme or a consonant pair. And the graphemes a language use for them is one more can of worms.