OP from what you’re saying they’ve given him a smaller area to work for the first couple of picks and have put a time limit on him improving to the same level as everyone else.
You said he has hyper mobility - does he experience pain and fatigue as a result of that? Because if so dot com may not be suitable long term, and combined with his ASD it will not only be tiring but also very stressful because of the expected work rate. Is that likely to make his overall health worse ?
The purpose of reasonable adjustment is to eliminate or minimise the effects of disability and It should be specifically tailored to the individual needs of the disabled person. If he feels that they didn’t pay much attention in the meeting when he mentioned his disability, and he hasn’t had the opportunity to tell them what he needs then they haven’t met the definition of reasonable adjustment - basically all they’ve they’ve done is the minimum necessary to get him up to speed and they’ve time limited it based on their operational needs.
Basically it’s all about what can be considered reasonable in the adjustments they make but ultimately If the role he’s in proves unsuitable and reasonable adjustment doesn’t solve the problem, then they also have a duty to consider whether any other more suitable roles exist for him within the company and if they do, to provide any training and support necessary for an alternative role
Sacking him should be the last resort. A large concern like Tesco should be aware of their responsibilities under the Equality Act 2010, including something called a Capability Procedure, which is a structured process with defined steps, including meetings, performance improvement plans, and reviews. The aim is to provide support and resources for improvement rather than the standard disciplinary procedure. Capability Procedures are appropriate when performance is affected by illness, or disability, or when reasonable adjustments have failed to enable the employee to meet required standards.
An initial meeting with the employer takes place to try to identify the reasons for performance issues, during which the employee is given the opportunity to talk about any issues caused by disability and what might be needed to resolve them. A Performance Improvement Plan (PIP) should then follow which will include specific goals, actions, and timelines to help the employee improve, and should include any necessary training and support required to achieve them.
There should be regular monitoring throughout an agreed time period, making adjustments to the PIP as needed. If the employee's performance doesn't improve as a result of these measures, the employer can then consider dismissal, but only after exhausting all other options.
You can see from the above that what happened at the meeting doesn’t meet the standard for Capability Procedure - instead DS appears to have been subject to an inappropriate disciplinary procedure. I would also argue that it was inappropriate for them to treat the problem with the holiday booking as a disciplinary because, again, they are aware he has a disability which may affect his information processing abilities, and they should have made sure he was aware the request had been rejected.
I think DS needs to communicate with his supervisor and also his union rep throughout his improvement period, to make sure that appropriate monitoring is carried out and he’s not just left to get on with it, and if he doesn’t meet the required standards at the end of it then he needs to ensure that the supervisor and union rep are aware of everything l’ve discussed here, so that they can help DS get the right level of support from his employer before they get as far as considering dismissal. If he does meet the standard and he feels that it’s unsustainable then he shouldn't wait until his performance is affected. He needs to communicate how he feels and ask for support.
Reasonable adjustment isn’t a favour OP, it’s the law. They knew he was disabled when they took him on, and now they have a legal responsibility to try to level the playing field so he has everything he needs to do the job.