It doesn't work like that. Wherever you obtained Figure 1, it is obvious that it wasn't done by STRING, as its style and format are completely different. If I were to guess, what's in Figure 1 appears to be old results that were plotted manually. I would not expect that STRING will reproduce the results that were done a long time ago or with a different set of interactions. Instead, I suggest you stick with the current plot, as it is more likely to be reliable. For example, when I start a search with SEC24C on STRING, it includes all the proteins you want, but that network doesn't seem to be connected with TMED2.
Thank you so much for your help!