First you can look these tests (specially about jitter)In these some tests have used SDG1010 and 1025.
In most of things they are same.
Look there jitter image 6. Made with two channels and ~93kHz square.
Then look image 4 and then image 7 with lower frequancies.
Also image 7 is made for jitter test so it is not good for look inside corner where signal rising edge start. I will test and take later some images with better settings for look inside this corner. (I have something allready but I can not use these - becouse images have something (done in third party lab) where I need follow NDA)
There are (of course) lot of "glitches" due to natural jitter and filtering. typically they stay "typically" below ~10% of signal level and around jitter p-p time before rising edge start (are not equally spaced throughout the time domain, but the emphasis on close to the rising edge (statistical distribution)).
For OP, please read also Agilent paper about this type of DDS generators principle. This is simple DDS generator and jitter is natural with this principle.
If you have real glitches what levels are nearly 50% (as shown in your one image) from signal level something is badly wrong. Something is wrong in your measurement OR something is wrong in your Siglent SDG OR both. Also you can set your oscilloscope trigger to level where it do not meet these "glitches". And for jitter, look next rising edge from triggering rising edge.
After I have enough time for do some tests with Siglent SDG I will show lot of better images about this corner before square rising edge in this image. This image here is not for this purpose, it is made for characterize amount of typical peak to peak jitter.
(it is typically as manufacturer specified). Filtering is always compromise but still it perhaps can do better without hop to next price group. Some amount of this corner impurity need accept. Just as we need also accept corners wobbling aliasing in oscilloscopes and many other natural things. If <0.5k$ machine is not enough good it can always buy 5k$ or 50k$ unit. But also if you get more accurate test equipments you find still (but more small) "errors" there. It is one important part of experience and knowledge to characterize what is fail and what is normal.
Also of course there is channel to channel jitter becouse both channels signal have jitter and now if you synchronize to other channel and look how other channel have jitter related to other channel - it is basic fundamental in this type of generator principle.
If need generator what do not have this this type of jitter then this generator type is wrong for your use. Also there are some golden frequancies where do not need "hop" for example adjust frequency or period (remember sampling rate).
If there is
really this level of glitches what your image show then your generator have some fail. Simply talking - then your generator is broken.
----
(Yes I'm also aghp (well known seller as "brand" in my country and specially in some group of peoples)
but now IF I find something what these companies do not want publish (data/hack/modification or other this kind of things) for Owon/Siglent I can not at all publish these becouse I'm both companies accepted reseller and service - if this is unethical - sorry, I keep these in my head. ; )
But original "accident" happend after some old customer and friend ask me why I'm rf-loop in EEVblog becouse I'm "aghp"... after 3 minute "thinking" it was ready... ok: now I'm aghp, satisfied now? What rf-loop or aghp have talk here: there is not any kind of discrepancy.
I did not destroy rf-loop account becouse I think it may be useful in future some situations IF there come data or something what seller can not publish without loose deal with manufacturer. ; ) ) Then also sometimes becouse I have several computers (some have same IP behind NAT and some in other locations and even some in China sometimes) Sometimes have happend accident that I open PC and go to EEVblog and I have not looked login (automatic) and just start write without thinkin who I'm becouse I'm myself always.
All know outside of equipment are not secrets.. and same for inside... all can measure and test these. But inside there may be things where can use some given information about repair service work.
Of course I can still publish errors and all information what is normal from seller who do not sell only "nice boxes". - rf-loop (aka and "official": aghp or aghp55)