What does a mechanic mean when he says: change transmission fluid both ways?
I presume that he means that he will use an exchange machine.
This hooks into the lines that fluid is pumped from the transmission to and from the cooler in the radiator.
For every used pint that is pumped out of the trans…a new pint is pumped into the trans to replace the used fluid.
This is not a universal term, so I’m just guessing.
Yosemite
I would take that to mean he is dropping the pan , changing the filter and then doing a fluid exchange.
Why not ask him?
Because that makes too much sense ? 
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I presume you have an automatic transmission. There’s two basic ways to remove the old fluid and put in new. The first way is to unbolt the transmission pan and allow all the old fluid to drain out, then clean the inside of the pan, inspect the bottom of the pan for metal debris (indicating a problem with the transmission innards), replace the filter, bolt the pan back on with a new gasket, and refill with fresh fluid. The problem with that method is that it drains less than half of the total fluid, b/c there are other places in the system that don’t get drained this way. The second method attempts to overcome that problem by hooking up a machine to the transmission fluid lines. Next they start and idle the engine so the transmission pump (part of the transmission) will pump the fluid out to the machine, and the machine return fresh fluid in its place. The problem with the second method is the inside of the pan isn’t cleaned, no inspection for metal debris, and the filter isn’t replaced. So some shops do it both ways in an attempt to solve both method’s problems.