They don't. Toyota doesn't produce any turbocharged engines in the suitable volume range 1.6-2.0 except one which is special engine operating in Atkinson't cycle, i.e. it is suitable as a range extender for hybrid cars but not as a base for racing engine because Atkinson's cycle sacrifices power per volume for fuel efficiency.
EA888 is codename for all recent 1.8TSI engines (whole family is designed by Audi). Chinese variants are somewhat modified compared to European ones but it's not different engine, just a modification of the same one as in Europe.
