The journey is Watton At Stone to Vauxhall. Pink readers doesn't mean a great deal to me. I'm aware that there are readers at barriers and readers internally at the interchange stations, but that's as much as I know.
Some stations have readers which are coloured pink, like so:

They are generally used to prove eligibility for a lower fare as mentioned.
Anyway it's not applicable to this particular example. The reason why you're being charged different amounts is that £15.30 is the peak fare and £9.20 is the off-peak fare.
Heading towards Vauxhall, the peak fare is charged if you touch in between 06:30 and 09:30. Off-peak fares apply throughout the rest of the day including in the evening, as it is deemed a contra-peak journey. Heading towards Watton, the peak fare is charged if you touch in between 06:30-09:30 or 16:00-19:00.
The time you touch in at the start of your journey (i.e. Vauxhall or Watton) is what determines whether you get charged a peak or off-peak fare. Subsequent touches after that point (e.g. at an interchange or at your destination) don't change the classification of the journey as peak or off-peak.
If you have a Network Railcard you can get a slight discount on your evening journey home by buying a paper ticket. The Railcard offers a 1/3 discount but has a minimum fare of £13 on weekdays. So you could buy a paper ticket for the £13 minimum fare in the evening, instead of paying the £15.30 PAYG peak fare. (The Network Railcard isn't valid before 10am on weekdays so it couldn't be used to get a discount in the morning)
You could get the full 1/3 discount by using a Gold Card. Any annual season ticket involving the Gold Card area (see
map) automatically gives you this. It's like a Network Railcard but slightly less restricted - there's no minimum fare, and it's valid from 9:30 instead of 10am.
The cheapest Gold Card-eligible annual season ticket costs £212 a year. So you'd have to weigh up whether the saving achieved by getting the full 1/3 discount instead of paying the £13 minimum fare is worth it, when you consider the £212 a year cost against the £35 a year cost of a Network Railcard.
The saving each day would be £2.45 (£13 Network Railcard minimum fare less £10.55 Gold Card fare) so you'd need to travel into London at least 73 times a year, or an average of around 1.5 times per week, for the saving to exceed the £177 additional upfront cost.
That makes sense, except that I appear to have tapped in at 06:32 for the off peak journey in, which appears to be inside peak time.
There is a few minutes' leeway from the advertised times, to allow for station clocks being incorrectly synchronised and/or trains running late. You are actually only charged peak fares from 06:35 to 09:27 and 16:05 to 18:57.