Softened pronunciation of consonants, such as "t" or "s" followed by "y"
Solution 1:
These are examples of the process called "palatalisation", which is very widespread in many languages round the world.
It happened in the history of English, for example to turn the /k/ in "kirk" into the /tʃ/ in "church". ("Kirk" survives in Scotland and northern England)
The phrases you described are pronounced without palatalisation in most or all varieties of English when spoken very carefully, but in normal speech many varieties of English do palatalise them.