Here is some lines I've used to set up a spectrogram with more control on how it is created. You should be able to use tStart to get what you need.
tStart=150; %seconds
fs=1000; %Hz
nfft=fs/binWidth; %samples
overlap = 50;%
fLimit=400; %Hz
T = 0:1/fs:2;
X = chirp(T,100,1,200,'q');
[~, f,t,P]=spectrogram(X,hann(nfft),nfft/(100/overlap),nfft,fs);
f(f>fLimit)=[];
t=t+tStart;
P=10*log10(P(1:length(f),:)');
sf=surf(f,t,P,'edgecolor','none');
view(0,90);
axis tight;
