No, the coax doesn't -have to be- all the way from both antennas to the radio, but depending on distances between all of those things it can be. Basically what you are doing is using that 75 ohm coax as am impedance matching transformer to provide an impedance of close to 50 ohms when both antennas are joined. That's called 'conjugate' matching, BTW. If those antennas are quite a ways from the antenna, then 'normal' 50 ohm coax from the join, or 'T', to the radio works just dandy.
It's not a very realistic idea to expect a "perfect" impedance match (SWR) with a phasing network like this. If it's something near 1.5:1 at the radio you're probably about as close as is practical. Why? 'Cuz the impedance of the antennas, and the feed lines are very seldom exactly what they are purported to be. If you can't do the measuring to determine those impedances then it's always just a guess. Sometimes you get lucky though...
- 'Doc