I don't know of any rule that requires all parts of a sentence to be in the same tense. I can think of many correct sentences where they are not. Two are:
"Once I was fat, but now I am thin."
"It rained yesterday, it's cloudy today, but tomorrow it will be sunny."
You could create two or three sentences from each of these, but they would be short and choppy. Sometimes that's a good style, as in this famous quote from Snoopy in Charles Schulz's "Charlie Brown" comic strip:
"Yesterday I was a dog. Today I'm a dog. Tomorrow I'll probably be a dog. There's so little room for advancement."
Often, however, that's not a good writing style. (Most of us do not draw comic strips and do not put words in the mouths of beagles.) In that case, I'd feel free to combine related ideas into one sentence. If those ideas are best expressed in different tenses, use those tenses, and don't worry about it.