I moved into my company dormitory at the same time I started my job.
My move to the company apartment coincided with the start of my job.
ーI moved into my company dormitory at the same time I started my job.
「仕事を始めるのと同時に会社の寮に引っ越した」
to move into で「〜に引っ越す」
company dormitory で「会社の寮」
at the same time で「同時に」
ーMy move to the company apartment coincided with the start of my job.
「会社のアパートへの引越しと就職は同時に起こった」
to coincide with で「〜と同時に起こる」
ご参考まで！
カナダ 
