That's right, the correct way to say is "он управляет тремя компаниями", "он управляет тремястами шестьюдесятью четырьмя сотрудниками". By the way, there is a site that can help you to incline the numbers.
Наименования и склонения числительных: склонение числительных по падежам онлайн
Notice, however, that this site is meant for the Russian-speaking people. It means, that a lot of Russians don't know how to incline long numbers. So quite often you can hear in a colloquial speech phrases, where numbers are used with wrong cases or in the nominative case, or one can incline only the last digit of the long number and leave the others in the nominative. This, however never applies to short numbers, which are always inclined very well.
So, you see, this part of the Russia grammar is difficult for the Russians themselves, so it is advisable to avoid phrases which demand the use of inclination of long numbers. Actually, there is always a way to rephrase a sentence, or to break a sentence in two so that the long number is used in the nominative case. For example:
"Под его управлением находятся триста шестьдесят четыре сотрудника".
Or:
"У него триста шестьдесят четыре сотрудника. Он всеми ими управляет."