If I understand your question correctly, I think you want to use the movmean function with the 'SamplePoints' option.
rng default
t = sort(rand(10, 1));
x = randi(10, 10, 1);
m = movmean(x, [0.25 0.125], 'SamplePoints', t);
results = table((1:10).', t, t-0.25, t+0.125, x, m, ...
'VariableNames', {'row', 't', 't_before', 't_after', 'x', 'movingAverage'})
As an example, consider row 3 of the results table. Row 3's movingAverage should consist of the mean of the values of x in all rows whose t values are between the values of t_before and t_after in row 3. For this sample code, I used rng default so you will receive the same t and x vectors as I did and thus I know that the first three rows contribute to row 3's movingAverage:
results{3, 'movingAverage'} - mean(x(1:3)) % should be 0
