Short answer:
The pink oyster reader did function correctly, in the sense that it has registered your journey as one that avoids zone 1. However, since you used a Southern service in between your journey, you are charged a mixed Transport for London (TfL) + National Rail (NR) fare instead, which is more expensive than a TfL-only journey.
The lesson to readers is hence: If your rail journey solely involves Transport for London (TfL) services (Underground, Overground, Elizabeth line within Greater London and DLR), involving one or more National Rail services in your journey may cost you more, and you should check before you travel and consider whether it is worth it.
This obviously does not apply if you have a Travelcard. Some other exceptions also apply - e.g, journeys on Thameslink core, c2c to Upminster/Rainham, Chiltern Railways to Amersham/West Ruislip, and GWR between West Ealing and Greenford are charged at TfL-only rate. See last section of the long answer.
Long answer:
What does the alternate fare route actually entail?
For this particular journey (Hayes & Harlington to Tooting Broadway), TfL presented the following way to avoid zone 1 in their single fare finder, which in my opinion, is slightly cryptic:
Avoiding Zone 1 via Clapham North/Clapham High Street, Clapham Junction and Shepherd's Bush (or West Brompton and Earl's Court)
(The latest version has stations in the correct travel order but is not materially different.)
This means you have two options in making this journey. Note an OSI below means an Out of Station Interchange - where you have to touch out and back into another physically separate station for an interchange:
Hayes & Harlington (Elizabeth line, then TfL Rail) >
Ealing Broadway (Central line) >
Shepherd's Bush LU (OSI to Shepherd's Bush LO for London Overground) >
Clapham Junction (London Overground) >
Clapham High Street (OSI to Clapham North for Northern line) >
Tooting Broadway
Hayes & Harlington (Elizabeth line, then TfL Rail) >
Ealing Broadway (District line) >
Earl's Court (District Line) >
West Brompton (London Overground) >
Clapham Junction (London Overground) >
Clapham High Street (OSI to Clapham North for Northern line) >
Tooting Broadway
Notice all legs in either journey only involve services that are under TfL control - Elizabeth line (then TfL rail), London Overground, and lines in London Underground.
Enter National Rail...
Now judging by the journey record, the OP is very likely to have chosen option 2 and touched on the pink reader in West Brompton. However, they took a slight deviation in route once they arrived at Clapham Junction:
- Hayes & Harlington (Elizabeth line, then TfL Rail) >
Ealing Broadway (District line) >
Earl's Court (District Line) >
West Brompton (London Overground) >
Clapham Junction (Southern) >
Balham NR (OSI to Balham LU for Northern line) >
Tooting Broadway
While it sounded like the OP just took another available train, they have inadvertently straddled the two very different systems, one under TfL's (and the Mayor of London's) control and one TfL has no control at all, including the fares.
As a result, the OP is charged a mixed TfL and NR fare, a fare scale charged when someone takes a journey involving both systems. This is always at least, and often higher than the fare charged when someone takes a journey using TfL's system only.
Oyster fare structure is a mess
I will start by quoting Mike Whitaker, a well-respected guy in the community who specialises in Oyster and rail fare. He had said on his site (emphasis mine):
Despite setting zonal fares a few years ago, the fare structure for rail journeys is incredibly complex and getting worse. TfL used to have a series of pages on their website which described the various scales in great detail. Unfortunately they decided that maintaining them was too complex, so they removed them.
He did the community a great service by sending many Freedom of Information requests to TfL to obtain, e.g. the fare information, and created an independent single fare finder which queries TfL's fare database with supplement information.
I encourage you to read his Guide to fare scales, which shows the five different kinds of fare with Oyster and contactless PAYG travel. It used to be worse - when this answer was first written, there were actually eight different kinds of fare with Oyster.
Alternatively (for those who want to avoid information overload), you can attempt to find the correct single journey fare using this table at the bottom of this page. One should use the "National Railcard/Gold Card" and "2018" options, "Off-peak" table, "Zones 2-5" row, and "NR1-T" column to find the correct fare for the OP's journey back in 2018, which is indeed £1.80.