I'm a retired optometrist, and it might just be that you're not fully adjusted to wearing the varifocals. It can take a couple of weeks to get used to a new prescription, particularly varifocals, or if there has been a large change in the prescription.
It could also be that the varifocal lenses are not quite in the correct position for how the glasses are adjusted. This is easy to correct by having a dispensing optician mark the lenses up and make sure that they are adjusted to sit in the correct place so that you are looking through the right part of the lenses for distance and near.
The other possibility (and one which can cause a shadowing effect) is that you have some astigmatism which hasn't been fully corrected, or that you've had a change in the correction for astigmatism. Astigmatism is where the eye is slightly more rugby ball shaped than round, meaning that you need two different corrections at right angles to each other. Most people have some astigmatism, so it isn't anything to worry about.
That said, you need to go back to Specsavers and ask them to check the glasses for you, and describe exactly what you are having trouble with, so they can have a look. If they are at all worried they will book you in with an optometrist again, to double check that the prescription is right. The fact that you feel it happens when you are fatigued leads me to think that it is either the change in prescription (you say it was a large change), or that the prescription isn't quite right for you (an eye test is subjective and therefore the answers given can vary depending on how the patient is feeling, how tired they are etc). If you had a brain tumour, you would be more likely to have the shadowing effect all of the time, (along with other symptoms) as tiredness wouldn't affect that.
Go and get it checked, it is most likely something really simple and easy to remedy.
I would like to address the suggestion that Specsavers' opticians are crap. I worked for Specsavers as an optometrist for my whole optometry career. I trained in exactly the same way as every other optometrist in the country, we all do the same degree/professional qualification regardless of whether we end up working for an independent or a chain, and we all have to maintain our training in order to remain registered with the General Optical Council, which we have to do in order to practise. There is a perception that because Specsavers is visible on the high street, and because they charge less than other places, that the opticians are inferior, but that isn't the case.