I edited Profiles Table at first (changed SpeedFactor values in some of the time spans), saved the edits, stoped edit session and solved Route again and saw that travel time for that route hadn't changed, even if I adjusted values in appropriate profile that it should had.
When I edited Streets-Profiles Table (I assigned different profile to egdes = changed values in appropriate field (in field connected to day of week I was using in analysis)), saved the edits and stoped edit session, the Build command on Network Dataset told me that "The network dataset has already been built."
When I changed Histroical profiles type to Time, I was able to Rebulid dataset. Then I switched Historical profile type back to Speed, Rebulit again and solved Route again and changes in tables were projected into travel time.
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And another one remark, the linkage between tables "Profiles" and "Streets-Profiles" is based on OBJECTID of particular profile. From documentation I supposed that ProfileID is taken as the Key for the relationship, but after testing I figured out that OBJECTID is used (that is same as in connection between edges and the Streets-Profiles Table, where OBJECTID (EdgeFID) is used, but that is clear from the documentation).
Thanks for help.
Filip