Hello, Yasmin!
 
The kind of assimilation that occurs when t and d are followed by /j/ is called YOD COALESCENCE. /d/ + /j/ becomes /dʒ/ while  /t/ + /j/ become /tʃ/. If the teachers you�re supervising produce  /dʒ/ instead of /tʃ/ when /t/ is followed by /j/, then they�re doing it wrongly; " let you out", for instance, must be /ˌletʃ u ˌaʊt/.
 
 YOD COALESCENCE also occurs in British English within a word, though not in careful RP.  Example: tune /tju:n/ can become /tʃu:n/. Meanwhile, when the j sound is in an unstressed syllable, this coalescence is often variable in British English but obligatory in American English. Example; factual /ˈf�ktjʊəl/ˈf�ktʃʊəl/.
 
 
Assimilation
 is very common in everyday speech. It usually happens at word 
boundaries, but it can also occur at the end of a syllable depending on 
the sound that follows.
 
-  Alveolar 
consonants t ,d, n, when they occur at the end of a word or syllable, 
can optionally assimilate to the place of articulation of the next 
syllable (�regressive� assimilation).
            Thus
 /n/ can become
 /m/ before 
p, b & 
m. Examples: ten men >
 /ˌtem ˈmen/; downbeat>
 /  daʊmˈbiːt/        
         2 /n/ can become /ŋ/ before k & g. Examples: fine grade > /ˌfaɪŋ ˈgreɪd/
            /d/ can change to b before a bilabial and g before a velar. Examples: red paint /ˌreb ˈpeiɪnt/, bad guys /ˌb�g ˈgaɪz/
 
         3 /t/ can change to /p/ and /k/, but a change to /t/ is more frequent, when followed by another consonant- though a  glottal  stop is even more common.  eight boys /ˌeɪp ˈbɔɪz/, /ˌeɪʔ ˈbɔɪz/ 
 
         4 /s/ and /z/ can change to ʃ and ʒ respectively, but only before /  ʃ/ and /j/. Example: this shape /ˌ�ɪʃ ˈʃeɪp/
 
Sometimes a consonant can assimilate  to the place of articulation of the preceding consonant (�progressive� assimilation).. In English, this applies only to Syllable n, changing it to syllabic m or ŋ as appropriate, provided there�s not a vowel after the nasal sound: Examples /ˈrɪbən/ becomes /ˈrɪbm/ & bacon /ˈbeɪkən/ becomes /ˈbeɪkŋ/
 
Some British English Speakers assimilate s to ʃ before tʃ and tr. Example; strong /ʃtrong/ instead of /strong/