Couple of reasons;
If you are comparing the affect of vaccination in the UK - only the over 65s have been vaccinated in great numbers at the time of the analysis, and above 65 they were vaccinated in decreasing age cohorts as graphed. I think under 65 vaccinations only begin after end of Feb in large numbers in UK?
If you are having trouble interpreting these graphs, particularly the Israel dataset which is larger, the magnitude of the decrease is not the most interesting part - it is the phasing of the peaks and the relative difference in the rate of decrease, both of which track the phasing of the age cohorts vaccinated.
edit: BTW the upper tweet is the Israel scientist who has been doing the timeseries analysis - the lower tweet is the one he is replying to in general agreement.