The embedded page is supposed to work that way, and if you want your analysis to load directly we need to use a slightly different URL in iframe. Check the below two options for more clarification:
<html><head></head> <!-- Option 1. You must refresh first --> <iframe src="http://mySpotfireServer/spotfire/wp/OpenAnalysis?file=/Introduction%20to%20Spotfire&options=7-1,8-1,9-1,10-1,11-1,12-1,13-1,14-1,1-1,2-1,3-1,4-1,5-0,6-0,15-1,17-1" width="800" height="600" ></iframe> <!-- Option 2. You must NOT refresh first --> <iframe src="http://mySpotfireServer/spotfire/wp/Embed?file=/Introduction%20to%20Spotfire&options=7-1,8-1,9-1,10-1,11-1,12-0,13-1,14-0,1-0,2-1,3-1,4-1,5-1,6-1,15-1" width="800" height="600" ></iframe>
The same is also demoed in the gif below: