I didn't see the technicians performing the actual beehive removal.
I didn't exactly see the bee control technicians getting rid of the beehives during their work.
I didn't exactly see the bee control professionals while they were removing the beehives.
"exactly" 「全く丁度」「その通りの」や、"actual"「実際の」などの単語が適当です。
「（Aが）〜をしている間」は、during ~, while A is doing ~, です。
I didn't see 「私は見ていない」
I didn't exactly see 「私はまさにその通りは見ていない」
see the bee control technicians getting rid of the beehives「蜂駆除業者の方々が蜂の巣を駆除するところを見る」
get rid of the beehives 「蜂の巣を駆除する」
remove the beehives 「蜂の巣を取り除く」
perform the beehive removal 「蜂の巣駆除を実行する」
日本 
