Will engineering schools at universities like UPenn, CalTech etc. reject my application if I have industrial internships that involve techno-management profiles rather than just research internships as an undergraduate?
For specific schools you need to ask them. However, in general, at the MS level in the US, I don't think that any sort of experience will harm your chances. Some may contribute more and some less, of course.
I would guess that even top universities in the US accept a lot of candidates with no experience at all beyond the BS/BA degree. Of course, the competition at such places is fierce with few seats available and many well qualified candidates.
But, if the purpose of your question is to pick which of two internships to accept, the research one might be marginally better. But who knows? Real world experience in engineering is pretty valuable.
If you have already done one of these then there is no question at all. Your record is what it is and it is up to you to present it in the best light.
The answer might be different at the doctoral level, of course, and may be different in other countries with different educational systems.