Is this a Bulb SMETS2 smart meter on a dual rate tariff, or is it a traditional Economy 7 meter?
If it’s a traditional meter, then switching supplier has no effect and it all still works however it did before, with the same rate switching times which varies by area. If the clock is wrong, then it needs to be reset by a contractor sent by the supplier. You can’t do it yourself, because if you could then obviously you could just keep changing it so it’s off-peak all the time. If the clock keeps going wrong, because it’s running at the wrong rate, then the meter is faulty and needs to be replaced. The clock does not change during summer time. The rate changes are controlled by the clock on the meter, and so you have to remember your rate changes are offset by one hour.
If it’s a Bulb SMETS2 smart meter, since Bulb do not officially support Economy 7 on their SMETS2 meters no one really knows how this will work. However, there are people reporting on here that they have E7 on their new SMETS2 meters, so Bulb must be doing it without officially saying it’s now available.
The night rate probably works like the the three-rate smart tariff. In which case it will switch 11pm to 7am, which I guess is really Economy 8. This could vary between supplier, as each will have their own Economy 7 (or equivalent) tariff. The clock does change between GMT and BST, and so your rate switches always happen at the same time through the year. The rate changes are still controlled by the clock on the meter as before. My IHD shows a 90 minute countdown to each rate change on the Bulb SMETS1 smart tariff trial.