Answer to my question seems to be in How Do You Do That book. I have to add though, that this book is in conflict with Core Rulebook on several occasions, mostly when it comes to setting up Sphere Level requirements for certain effects.
With this being said, quoting page 79 in How Do You Do That, the answer is as follows:
• Although each manifested “self” has its own physical
integrity, all “selves” return to the original mage when
the spell’s Duration ends. Each “self” takes damage
normally, as if each copy was a character in its own right.
• If several selves take damage, this might be fatal if and
when all that damage gets added up in the original
mage’s Pattern. Game-wise, every level of damage taken
by a “self” winds up on the mage’s Health track if the
mage re-integrates while several “selves” are hurt.
• That said, only the death of the original “self” will
kill all the duplicates. Individual duplicates can die,
and although their injuries no longer get added to the
original character’s Health track, each “duplicate death”
inflicts one aggravated health level of damage on the
original character. This damage can’t be healed until
all of the “selves” have been reunited into the original
mage. And so, it’s in his best interest to keep them all
alive. If the mage has eight duplicates, and all eight of
them are killed, that mage immediately dies.
So essentialy, as long as less than 8 copies die, this can be repeated and aggravated damage from their deaths healed after reintegration. Same goes for damaged selves, it hurts but can be healed after reintegration. There's also nothing that says reintegrating copies can't be done one at a time, which makes managing reintegrated damage even easier.
After reading this I have to mark previous answer as incorrect, because health bars are, in fact, separate.