there need to be explained more details to answer

1)species of jasmin(if you know)
2)how large is the pot and how large the 2 plants in it?
3)when exactly did the leaves begin to dry?
4)its exposure
5)have you noticed that also in the previous year?(in a less extent)
6)do you water it regurarly?You mentioned that you watered it now, in the winter.How often?
7)what's the composition of soil?
8)for how long have both plants been together?
9)have you fertilize it lately?if so,what kind of fertilizer?

Although there are innumerable reasons as to why the leaves can be dried, I'll try to make a guess.
But please explain a little more to us please

Hope that helps. Some of the lower leaves have dried up tips now as well. I have an automated watering system but I also top up some large pots (like this one) with the hose once per week in the winter time. I don't let the soil dry out, I that's what you're asking.
Thanks again for the interest and Kalo Pasca!

I'd like you to exclude some cases first

any frost damage(yes I know we had a very mild winter, an uprecedented one)

any possible damage caused by nebulizing with any kind of chemical a neighbouring plant(not necessarily yours)and the wind drawed away some of it towards your plant

I suppose there are 2 possibilities for the damage(just supposing though)
First there may be some bacterium infecting your jasmin.Oleacae family(not the only one) is well known to catch lots of bacteriums.The warm winter in conjunction with a little moisture in the air may have caused all that fuss on your plant
Secondly there may very well be some WORMS in the soil.Look for any water keeping up under your jerdiniere or try to move a little the pot and see if there are any micro- or macroscopic worms under it.If so, there is a possibility of that being the problem.

Another theory would be the allelopathy effect.It may be simple, those 2 plans can't grow together in a pot.I think Rhynchospermum would overwhelm your Jasminun one day no matter your Jasmin regains its health.

Just try to remove all dead parts of your plant, both stems and leaves.Spray it with Copper(biological pesticide) and see what happens.Move the pot also to see what's going on underneath(if it's removable).

Sorry but I haven't anything else to say.Maybe someone else here may give you some better advice on that.

Kalo pascha kai se sena
Ciao!!!!!