Starting in R2019a, heatmaps interpret text using TeX markup instead of displaying the literal characters. Therefore it seems you are using a release earlier than R2019a. Therefore, upgrading to the latest release might help!
For displaying "xlable values as yearly (1971,1972,...)" use the code below
close all; clc;
tbl = readtable('heatmapTest.xlsx');
t1 = datetime(1971,1,1);t2 = datetime(1986,12,1);
t = t1:calmonths(1):t2;t= t(:);
xlabels = string(datestr(t,10));
xlabels = char(xlabels);
xlabels = cellstr(xlabels);
ylabels = {'A_b' 'B_b' 'C_b' 'D_b'};
cdata = tbl{:,2:5};
h = heatmap(cdata');
h.XDisplayLabels = xlabels;
h.YDisplayLabels = ylabels;
idx = [true;diff(year(t))] ~=0;
h.XDisplayLabels(~idx) = {''};
