Short answer:

Nothing particular to Russian culture-- the Eastern Mediterranean enjoyed a reputation as disease-ridden throughout the 19th and into the early 20th century

Discussion:

The Ottoman Empire and Eastern Mediterranean enjoyed a grim reputation at the end of the 19th century. The Eastern Question and the stereotype of "the fatalistic Turk" were a commonplace.

Here's Karl Marx, writing in 1853

Turkey is the living sore of European legitimacy. The impotency of legitimate, monarchical government, ever since the first French Revolution, has resumed itself in the one axiom: Keep up the status quo. A testimonium paupertatis, an acknowledgment of the universal incompetence of the ruling powers, for any purpose of progress or civilisation, is seen in this universal agreement to stick to things as by chance or accident they happen to be.

The Eastern Mediterranean enjoyed a grim reputation for disease, particularly plague. The European International Sanitary Conventions were substantially to arrange for quarantines for ships arriving from plague-rife ports like Alexandria.

The 19th century international hygiene diplomatic record is filled with communications like Lord Ponsonby's letter to the Prime Minister

With reference to the proposed [Ottoman quarantine] regulations, I have to instruct your Excellency to endeavour strongly to impress upon the Turkish government that they would more effectually prevent the breaking out and spreading of the plague by introducing cleanliness and ventilation in the city and suburbs of Constantinople, than by any such violent interference as is proposed with the domestic arrangements of families. It is quite certain that the plague is much aggravated, if not actually generated, by the wants of cleanliness in the streets, by the want of sufficient ventilation in houses, and by the want of proper drainage in places contiguous to habitation;

You may have heard the term cordon sanitaire -- this term derives from boundaries around the Ottoman Empire, and the Austrians maintained a strict watch on their borders

As for persons, their treatment depended on the degree of danger expected. The Austrian government maintained an extensive, if not always reliable, plague intelligence service in the Ottoman Empire, relying on reports of special observers, consular agents, and the interrogation of travellers. When an outbreak was reported, the vigilance of the cordon was stepped up. Sentries were stationed at closer intervals and persons and goods detained for longer periods. There were three alert stages. In normal times, with no plague reported, the cordon was manned by four thousand men and the quarantine lasted for twenty-one days. If plague was suspected, the second stage went into effect. The cordon watch was reinforced to seven thousand men and the quarantine extended to twenty-eight days. Finally, when plague was confirmed, the cordon was guarded by eleven thousand men and the quarantine period lasted forty-eight days

So that was the reputation at the time. The Zionist arrivals' impressions weren't anything out of the ordinary. They were likely exacerbated by susceptibility to malaria-- new arrivals from northern climes likely got substantially sicker than inhabitants of long standing, both because of susceptibility and because of location of settlement. Here's an assessment by a physician writing in the British Medical Journal in 1931

In practically every instance where a large number of non-immunes have been introduced into a highly malarious region the new arrivals have suffered most severely, and the disease has taken its toll in sickness and in human life. The determined attempt by communities of Jews to colonize in Palestine might almost have been doomed at its inception, and, indeed, because of the prevailing hyperendemic conditions might have proved a most disastrous failure, had it not been for the particularly able manner in which defensive measures were gradually introduced. In the near future it will be no empty claim that country-wide malarial control has been established.

{snip}

The Jewish colonists most frequently settled in the neighbourhood of that precious commodity, water, with the result that in a very short time malaria was rife, and, as in the village of Hulda, the settlements could only be maintained by annual replacement of part of the population.

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See:

PLAGUE AND QUARANTINES IN THE COLONIAL ERA.” Plague, Quarantines and Geopolitics in the Ottoman Empire, by BİRSEN BULMUŞ, Edinburgh University Press, Edinburgh, 2012, pp. 130–151.

Bynum, W.F. “Policing Hearts of Darkness: Aspects of the International Sanitary Conferences.” History and Philosophy of the Life Sciences, vol. 15, no. 3, 1993, pp. 421–434.

ROTHENBERG, GUNTHER E. “The Austrian Sanitary Cordon and the Control of the Bubonic Plague: 1710-1871.” Journal of the History of Medicine and Allied Sciences, vol. 28, no. 1, 1973, pp. 15–23.

Control Of Malaria In Palestine.” The British Medical Journal, vol. 2, no. 3698, 1931, pp. 954–954.