In fluent speech, the conjunction (the first "that") is unstressed, and as a result some speakers reduce the vowel a bit toward schwa. However, if you told those speakers to carefully pronounce each word, I bet they would pronounce the conjunction and the pronoun the exact same same. A more common example of this kind of reduction is the word "to", which is almost always reduced to /tə/ ([tə] ~ [tʊ] ~ [ɾə] depending on dialect and surrounding words) in everyday speech when unstressed.

Fun fact, you can reduce just about every unstressed vowel in English to schwa (if it's not already a schwa) and still be largely understood.