Most probably, the image the designer has is a TIFF and he/she saved it as a jpg in order to send it to you. The Tiff isn't "embedded" within the JPG, merely the data started as Tiff data and was then converted (compressed) to the JPG algorithm (format).
The EXIF data is merely showing the format the image started in, the editing app, and the operating system along with other information, not data. The fact that "tiff" is mentioned in the EXIF information is no more valuable than the fact that "Macintosh" or "Adobe" are mentioned.
JPG and Tiff are a separate and independent compression algorithms.
JPG is a lossy compression scheme. Each time a JPG is saved, data is thrown out and lost. NEVER save a JPG as a JPG again.
Tiff is not a lossy compression scheme. Saving a tiff does not throw out any data.
You typically can't "extract" a tiff from a jpg.
JPG is a common format used for transferring images due to file sizes. It is not uncommon for a designer to work on and use Tiff images, then save them as a JPG, set at maximum quality, in order to reduce the file size for email or delivery. JPG has a better, but far more destructive, compression scheme. At a "maximum" quality setting, one save to JPG doesn't lose much data and is generally fine.
However, much of the tiff data can be seen as superfluous in the JPG format and therefore throw out when the JPG is saved. Such data is never secretly embedded because doing so would balloon the size of the JPG, which is in direct contradiction to the reasoning why JPG is useful.
You may be able to open the jpg in Photoshop and resave it as a Tiff.
Opening the jpg in Photoshop and using
Image > Image Size from the menu to check the resolution of the file may tell you a great deal more.
A jpg measuring 150x83px @300PPI works out the roughly a .5" x .25" image at print resolution. I do not know if that print size helps at all or how it may relate to what you are seeking. Or even if the file itself has a resolution of 300ppi. Anything less than 300ppi or if you need a file with dimensions larger than .5"x.25" and it would be evident the image is unacceptable for print production. But, I have no clue what the intention is as far as actual use of the image.
File size (kb) does not really have a direct correlation to the file contents. It's possible to have a multi-colored JPG that does not compress a great deal resulting in a larger file size(kb). Whereas an image with large fields of the same color will compress far more in the JPG format, resulting in smaller file sizes (KB).