Pick the length
When you play against pace bowlers on Indian pitches, the first thing you need to decipher is the line. Since the bounce is generally lower than it is outside the subcontinent, it's important to play the right lines - you can only leave balls that are clearly outside off, and you want to be playing across the line only if you're certain that the ball is missing the leg stump.
The lack of bounce covers up small errors in judgement of length, as long as you're looking to play off the front foot (it is possible in India to negotiate the short ball off the front foot). But a slight error in reading the line could prove fatal.
In Australia, the big adjustment one has to make is to read the length before reading the line. While picking the line is equally important (you don't want to play balls that can and should be left alone), reading the length correctly can often make up for errors in reading the line, because the extra bounce on Australian pitches takes the ball over the stumps more often than not. The percentages of lbw and bowled dismissals against pace are significantly lower in Australia than in India. It is possible to use the extra bounce to your advantage as a part of your defensive game in Australia
Have a defensive game against the short ball
While having a solid defensive game against bouncers is important in most Test matches, it's almost vital in Australia. The lack of pace and bounce on Indian pitches discourages the faster bowlers from digging in too short. So you can get away with a good attacking game and a not-so-efficient defence against bouncers. Also, in India the grounds aren't big enough to allow the bouncer trap to be executed well - even mishits end up going over the ropes.
In Australia, though, conditions are right for the bouncer. As a fast bowler, the moment you see a batsman taking you on, you can look to set up the bouncer trap. And the sizes of the grounds mean that bowlers can persist with that length longer than in other places. It's almost impossible to hit your way out of a bouncer trap in Australia, and so the likes of Prithvi Shaw and Rishabh Pant must find a defensive method to deal with the barrage of bouncers they are likely to face.
Choose between horizontal or vertical bat
The extra pace and bounce on Australian pitches make for positive shot-making, since the ball comes on to the bat nicely. But your shot selection needs to be spot-on; you must choose, and choose quickly, between vertical- and horizontal-bat shots for every delivery you face. On slow and low Indian pitches you get away with an angled bat, but that's a recipe for failure on pitches that offer more bounce and pace.
"The low percentage of bowled and lbw dismissals above paints a certain picture, but that has little to do with the length and plenty to do with the extra bounce on Australian pitches"
Look for the full ball
This won't count as an adjustment for Indian batsmen, because they are hardwired to be ready for the fuller delivery against pace. But when Indian batsmen tour down under, there's a lot of advice that comes their way telling them to work more on their horizontal-bat shots - the reason being that the Australian quick bowlers bowl the shorter length more often. This couldn't be further from the truth. The low percentage of bowled and lbw dismissals above paints a certain picture, but that has little to do with length and plenty to do with the extra bounce on Australian pitches. Most dismissals against pace, even in Australia, are while playing off the front foot, and so it's prudent to prepare for the full ball always. The short ball is used liberally to push the batsman back to set up a dismissal off the full ball, and seldom with the intent to take wickets through intimidation (unless you have shown a weakness against the short ball).
Keep the hands high while defending against spin
One big adjustment batsmen from the subcontinent need to make while playing against spin in Australia is to get the hands higher when playing the defensive stroke. Playing on pitches with low bounce, you often develop the habit of staying low while defending. In Australia that can lead to the ball hitting the shoulder of the bat or the gloves.
Also, scoring more runs off the back foot is an option one must be ready to explore, because playing a horizontal-bat shot against spin in India is an option if only the ball is a half-tracker, but in Australia, slightly short of good-length deliveries will also present opportunities for horizontal-bat scoring shots.