I don't think the leaves will have started changing colors yet.
The tense in the dependent clause [(that) the leaves will have started changing colors yet] is the Future Perfect Progressive (Continuous): will have or shall have been going
: will have started changing = : will have been changing
The past participle of be is been
The past AND past participle of start is started
"The progressive forms of the verb are not a separate tense. Progressive forms are made up of the various tenses of he verb be plus the present participle. Progressive forms are used to show continuing action."—John E. Warriner. Warriner’s English Grammar and Composition. Fifth Course. Liberty Edition. Orlando, Florida: Harcourt, Brace, and Jovanovich. 1986.
The Future Perfect Tense (will have or shall have + past participle)
"...will have started..."
The Future Perfect Progressive (Continuous) (will have or shall have + past participle + present participle)
"...will have started changing..."
Summary: You may substitute "started" using it in its past participle form for "been" which is the past participle of be
Furthermore, the future perfect tense is used to express action which will be completed in the future before some other future action or event. "leaves will have started (this happens before the changing of the colors)
With the progressive form the action which will be completed in future before some other future action or event is continuous. "leaves will have started changing (the process of started and changing colors is not a completed process; it is continuing over and over, an ongoing process, an action that will continue up until some time in the future)
Each of the six tenses has an additional form called the progressive
form, which expresses continuing action. It consists of the form of
the verb be plus the present participle of the verb.
Remember: The progressive is not a separate tense but an additional
form of each of the six tenses in the conjugation.
John E. Warriner. Warriner’s English Grammar and Composition. Third Course. Liberty Edition. Orlando, Florida: Harcourt, Brace, and Jovanovich. 1986. 196.
I don’t think the painters will have begun painting the house yet.
The stars in the sky will have appeared shining brighter in the fall.
The artist will have tried sculpturing a new model before he completes the old one.